CENTER OF MASS AND MOMENT OF INERTIA 1<
2. Find the center of mass of a right circular cone whose densi varies inversely as the square of the distance from the apex, the distan being measured along the axis.
dm = r • iry2 • dx
= ^'7T
Tlira
•dx
where n is the density at a unit distance from the apex. Therefore
1 ~h
• ( xdx
n
h'2 h '' 2
• f dx
•S n
FIG. 82.
PROBLEMS.
1. Find the center of mass of a right circular cone, the density of whi varies inversely as the distance from the vertex.
2. Find the center of mass of a circular plate, the density of whi varies as the distance from a point on the circumference.
3. Find the center of mass of a cylinder, the density of which var with the nth power of the distance from one base.
4. Find the center of mass of a quadrant of an ellipsoid.
6. Find the center of mass of a hemisphere, the density of which var as the distance from the center.
119. Center of Mass of a Number of Bodies. — Let mi; w
etc., be the masses and Xi, x2, etc., be the ^-coordinates of ti centers of mass of the individual bodies. Then if x denot the re-coordinate of the center of mass of the entire syste we can write
xdm